Finite Group Databasebeta

← #29684441

Subgroups — #29684441

Order 15616.

738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454617C211yesmaximal, characteristic
2#21454468C211yesmaximal, characteristic, complemented
3#21446711C211yesmaximal, characteristic
4#21446706C211yesmaximal, characteristic
5#21446569C211yesmaximal, characteristic, complemented
6#21446564C211yesmaximal, characteristic, complemented
7#21446533C211yesmaximal, characteristic, complemented
8#21446529C211yesmaximal, characteristic, complemented
9#21446526C211yesmaximal, characteristic, complemented
10#21446522C211yesmaximal, characteristic, complemented
11#21445726C211yesmaximal, characteristic, complemented
12C4×#14519703C211yesmaximal, characteristic, complemented
13C4×#14519704C211yesmaximal, characteristic, complemented
14#97×Dic61C211yesmaximal, characteristic, complemented
15C61×#2923C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16839872C412yescomplemented
19#16839867C412yescomplemented
20#16839862C412yescomplemented
21#16839860C412yescomplemented
22#16839824—22no—
23#16839817—22no—
24C2×#14519712C2211yescharacteristic
25C2×#14519712C2211yescharacteristic
26#16839798C2211yescharacteristic
27#16839788C2211yescharacteristic
28#16839788C2211yescharacteristic
29C2×#14519704C2211yescharacteristic
30C2×#14519704C2211yescharacteristic
31C2×#14519703C2211yescharacteristic
32C2×#14519703C2211yescharacteristic
33#16839758C2211yescharacteristic
34#16839756C2211yescharacteristic
35#16839728C2211yescharacteristic
36#16839728C2211yescharacteristic
37C4×#11758194C2211yescharacteristic
38C2×#14519688C2211yescharacteristic
39C2×#14519687C2211yescharacteristic
40C2×#14519687C2211yescharacteristic
41C2×C8×Dic61C2211yescharacteristic
42C2×C8×Dic61C2211yescharacteristic
43C42×Dic61C2211yescharacteristic
44#16839526C2211yescharacteristic
45#16839526C2211yescharacteristic
46#16839523C2211yescharacteristic
47#16839523C2211yescharacteristic
48#16839521C2211yescharacteristic
49#16839521C2211yescharacteristic
50C4×#41×C61C2211yescharacteristic
51C61×#433—22no—
52C61×#432—22no—
53C61×#424C2211yescharacteristic
54C61×#424C2211yescharacteristic
55C61×#408C2211yescharacteristic
56C61×#408C2211yescharacteristic
57C4×M16×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C2×#11758222C2311yescharacteristic
60#14519797—22no—
61#14519797—22no—
62C2×#11758202C2×C411yescharacteristic
63C2×#11758200C2×C411yescharacteristic
64C2×#11758201C2×C411yescharacteristic
65C2×#11758199C2×C411yescharacteristic
66C2×#11758194C2311yescharacteristic
67C2×#11758194C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C4×Dic122C2×C412yes—
71C4×D244C2×C412yes—
72C4×C22⋊D61—22no—
73#14519736C2311yescharacteristic
74#14519734—21no—
75C2×C4×Dic61—22no—
76C2×C4×Dic61C2311yescharacteristic
77C2×C4×Dic61C2311yescharacteristic
78C42×D61—21no—
79#14519712—22no—
80#14519712—22no—
81#14519710C2×C412yes—
82#14519708C2×C412yes—
83#14519706—22no—
84#14519706—22no—
85#14519704—22no—
86#14519704—22no—
87#14519703—22no—
88#14519703—22no—
89#14519701C2×C412yes—
90#14519700C2×C412yes—
91#14519698C2×C412yes—
92#14519697C2×C412yes—
93#14519689—22no—
94#14519689—22no—
95#14519688—21no—
96#14519688C2×C412yes—
97#14519688C2×C412yes—
98#14519687—22no—
99#14519687—22no—
100C4×#92418—21no—
101C8×Dic61—22no—
102C8×Dic61—22no—
103C2×#41×C61C2311yescharacteristic
104C2×M16×C61C2311yescharacteristic
105C2×M16×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C4×Q8×C61C2×C412yes—
109C4×D4×C61—22no—
110C4×D4×C61C2×C412yes—
111#117×C61—21no—
112#117×C61C2311yescharacteristic
113C2×C42×C61—21no—
114C2×C42×C61C2311yescharacteristic
115C4⋊C8×C61—22no—
116C4⋊C8×C61—22no—
117C22⋊C8×C61—22no—
118C22⋊C8×C61—22no—
119#97×C61—21no—
120#97×C61D412yes—
121#97×C61D412yes—
122C4×C8×C61—21no—
123#41×C61—21no—
124#41×C61—21no—
125#41×C61—21no—
126#41×C61—21no—
127C2×Q8×C61C22×C411yescharacteristic
128C2×D4×C61—21no—
129C2×D4×C61C22×C411yescharacteristic
130C22×C4×C61—21no—
131C22×C4×C61—22no—
132C22×C4×C61#4112yes—
133C22×C4×C61C2411yescharacteristic
134C2×C22⋊D61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137#11758222—21no—
138#11758222—21no—
139#11758222—21no—
140#11758222—21no—
141C2×D244C22×C411yescharacteristic
142C2×C4×D61—21no—
143C2×C4×D61—22no—
144C2×Dic122C22×C411yescharacteristic
145M16×C61—21no—
146M16×C61—21no—
147M16×C61—21no—
148M16×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61C2×D412yes—
156C2×C8×C61C2×D412yes—
157C4⋊C4×C61—22no—
158C4⋊C4×C61C22×C412yes—
159C22⋊C4×C61—21no—
160C22⋊C4×C61—22no—
161C42×C61—22no—
162C42×C61—21no—
163C42×C61C22×C412yes—
164C42×C61C2×D411yescharacteristic
165C42×C61C2×D411yescharacteristic
166C22⋊Dic61—21no—
167#11758202—22no—
168#11758201—22no—
169#11758200—22no—
170#11758199—22no—
171#11758198—22no—
172C4⋊Dic61C22×C412yes—
173#11758196—22no—
174C4×Dic61—22no—
175C4×Dic61—21no—
176C4×Dic61—21no—
177C4×Dic61—21no—
178C4×Dic61—44no—
179C4×Dic61#4112yes—
180C4×Dic61#4112yes—
181#11758194—21no—
182#11758194—21no—
183#11758194—21no—
184#11758194—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418C22×C412yes—
190C2×#92418C22×C411yescharacteristic
191C2×#92418C22×C411yescharacteristic
192C2×#92418#4112yes—
193C2×#92418#4112yes—
194C23×C61—21no—
195C23×C61C2×#4111yescharacteristic
196C22×D61—21no—
197Q8×C61—21no—
198Q8×C61—21no—
199D4×C61—21no—
200D4×C61—21no—
201D4×C61—41no—
202D4×C61—41no—
203C2×C4×C61—22no—
204C2×C4×C61—21no—
205C2×C4×C61—42no—
206C2×C4×C61—41no—
207C2×C4×C61—41no—
208C2×C4×C61—82no—
209C2×C4×C61C4×D412yes—
210C2×C4×C61C4×D412yes—
211C2×C4×C61C23×C411yescharacteristic
212C2×C4×C61C22×D411yescharacteristic
213C2×C4×C61C2×#4111yescharacteristic
214C2×C4×C61C2×#4111yescharacteristic
215C2×C4×C61C2×#4111yescharacteristic
216C2×C4×C61C2×#4111yescharacteristic
217C22⋊D61—41no—
218C22⋊D61—41no—
219C2×Dic61—24no—
220C2×Dic61—22no—
221C2×Dic61—21no—
222C2×Dic61—22no—
223C2×Dic61—22no—
224C2×Dic61—42no—
225D244—21no—
226D244—21no—
227C4×D61—41no—
228C4×D61—41no—
229C4×D61—82no—
230Dic122—21no—
231Dic122—21no—
232C8×C61—22no—
233C8×C61—22no—
234C8×C61—41no—
235C8×C61—41no—
236#92418—22no—
237#92418—41no—
238#92418—41no—
239#92418#11712yes—
240#92418#11712yes—
241#21297—611nomaximal, Sylow
242C22×C61—22no—
243C22×C61—42no—
244C22×C61—41no—
245C22×C61C2×C4×D411yescharacteristic
246C22×C61#52911yescharacteristic
247C22×C61#52911yescharacteristic
248C2×D61—42no—
249C2×D61—41no—
250C4×C61—22no—
251C4×C61—22no—
252C4×C61—42no—
253C4×C61—41no—
254C4×C61C2×#11711yescharacteristic
255C4×C61C4×#4111yescharacteristic
256C4×C61#53211yescharacteristic
257C4×C61#53211yescharacteristic
258Dic61—24no—
259Dic61—42no—
260Dic61—42no—
261Dic61—41no—
262#2943—611no—
263#2923—611no—
264#2923D6111yescharacteristic, complemented
265#1975—611no—
266#1974—611no—
267#1946—611no—
268#1945—611no—
269#1938—611no—
270#1938—611no—
271#1937—611no—
272#1937—611no—
273#1778—611no—
274C4×#104—611no—
275C4×#104—611no—
276C4×#97—611no—
277C2×C61—21no—
278C2×C61—21no—
279C2×C61—81no—
280C2×C61#229311yescharacteristic
281C2×C61#295612yes—
282D61—81no—
283C2×#135—611no—
284C4×#41—611no—
285C4×#41C2×D6111yescharacteristic
286#442—612no—
287#441—612no—
288#440—612no—
289#440—612no—
290#433—22no—
291#433—1222no—
292#432—22no—
293#432—1222no—
294C2×#108—611no—
295C2×#108—611no—
296#427—611no—
297#424—611no—
298#424—611no—
299#424C2×D6111yescharacteristic
300#424C2×D6111yescharacteristic
301C2×#104—611no—
302C2×#104—611no—
303C2×#104—611no—
304C2×#104—611no—
305#416—611no—
306#416—611no—
307#408—611no—
308#408—611no—
309#408C2×D6111yescharacteristic
310#408C2×D6111yescharacteristic
311C4×M16—611no—
312C4×M16C2×D6111yescharacteristic
313C2×#97—611no—
314C2×#97—611no—
315C2×#97—611no—
316C2×#97C2×D6111yescharacteristic
317C2×C4×C8—611no—
318C2×C4×C8—611no—
319C43—611no—
320#341—611no—
321#341—611no—
322#339—611no—
323#339—611no—
324#339—611no—
325#339—611no—
326C61#2129711yescharacteristic, complemented, Sylow
327C2×#41—611no—
328C2×#41C22×D6111yescharacteristic
329#135—1222no—
330#135—1222no—
331C2×Q16—611no—
332C2×SD16—611no—
333C2×SD16—611no—
334C2×D8—611no—
335C2×M16—611no—
336C2×M16—611no—
337C2×M16C22×D6111yescharacteristic
338C2×M16C22×D6111yescharacteristic
339C22×C8—611no—
340C22×C8—611no—
341C22×C8C22×D6111yescharacteristic
342C22×C8C22×D6111yescharacteristic
343C4×Q8—612no—
344C4×Q8C4×D6112yes—
345C4×D4—22no—
346C4×D4—612no—
347C4×D4—1222no—
348C4×D4C4×D6112yes—
349#117—21no—
350#117—611no—
351#117—1221no—
352#117C22×D6111yescharacteristic
353C2×C42—21no—
354C2×C42—611no—
355C2×C42—611no—
356C2×C42—1221no—
357C2×C42—1222no—
358C2×C42C22×D6111yescharacteristic
359#108—1222no—
360#108—1222no—
361#107—612no—
362#106—612no—
363C4⋊C8—22no—
364C4⋊C8—22no—
365C4⋊C8—1222no—
366C4⋊C8—1222no—
367#104—1222no—
368#104—1222no—
369#104—1222no—
370#104—1222no—
371#103—612no—
372#103—612no—
373#102—612no—
374#102—612no—
375C22⋊C8—22no—
376C22⋊C8—22no—
377C22⋊C8—1222no—
378C22⋊C8—1222no—
379#97—21no—
380#97—612no—
381#97—612no—
382#97—1222no—
383#97—1222no—
384#97—1221no—
385#97C22⋊D6112yes—
386#97C22⋊D6112yes—
387C4×C8—21no—
388C4×C8—1222no—
389C4×C8—1222no—
390C4×C8—1221no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—21no—
395#41—1221no—
396#41—1221no—
397#41—1221no—
398#41—1221no—
399C2×Q8—611no—
400C2×Q8C2×C4×D6111yescharacteristic
401C2×D4—21no—
402C2×D4—611no—
403C2×D4—1221no—
404C2×D4C2×C4×D6111yescharacteristic
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—1221no—
408C22×C4—1221no—
409C22×C4—1222no—
410C22×C4—1221no—
411C22×C4#1175822212yes—
412C22×C4C23×D6111yescharacteristic
413Q16—1222no—
414SD16—1222no—
415SD16—1222no—
416D8—1222no—
417M16—21no—
418M16—21no—
419M16—21no—
420M16—21no—
421M16—1221no—
422M16—1221no—
423M16—1221no—
424M16—1221no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—611no—
432C2×C8—611no—
433C2×C8—612no—
434C2×C8—612no—
435C2×C8—612no—
436C2×C8—1221no—
437C2×C8—1221no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8C2×C22⋊D6112yes—
441C2×C8C2×C22⋊D6112yes—
442C4⋊C4—22no—
443C4⋊C4—612no—
444C4⋊C4—1222no—
445C4⋊C4C2×C4×D6112yes—
446C22⋊C4—21no—
447C22⋊C4—22no—
448C22⋊C4—1221no—
449C22⋊C4—1222no—
450C42—21no—
451C42—22no—
452C42—612no—
453C42—612no—
454C42—1221no—
455C42—1221no—
456C42—1221no—
457C42—1222no—
458C42—2444no—
459C42C2×C4×D6112yes—
460C42C2×C22⋊D6111yescharacteristic
461C42C2×C22⋊D6111yescharacteristic
462C23—21no—
463C23—1221no—
464C23C2×#1175822211yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—1221no—
468Q8—1221no—
469D4—21no—
470D4—21no—
471D4—41no—
472D4—41no—
473D4—1221no—
474D4—1221no—
475D4—2441no—
476D4—2441no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—82no—
483C2×C4—1224no—
484C2×C4—1222no—
485C2×C4—1222no—
486C2×C4—1221no—
487C2×C4—1222no—
488C2×C4—4882no—
489C2×C4—2442no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4C4×C22⋊D6112yes—
493C2×C4C4×C22⋊D6112yes—
494C2×C4C22×C4×D6111yescharacteristic
495C2×C4C22×C22⋊D6111yescharacteristic
496C2×C4#41×D6111yescharacteristic
497C2×C4#41×D6111yescharacteristic
498C2×C4#41×D6111yescharacteristic
499C2×C4#41×D6111yescharacteristic
500C8—22no—
501C8—22no—
502C8—41no—
503C8—41no—
504C8—612no—
505C8—612no—
506C8—1222no—
507C8—2441no—
508C8—2441no—
509C22—22no—
510C22—41no—
511C22—42no—
512C22—2441no—
513C22—2442no—
514C22C2×C4×C22⋊D6111yescharacteristic
515C22#1684029011yescharacteristic
516C22#1684029011yescharacteristic
517C4—22no—
518C4—22no—
519C4—41no—
520C4—42no—
521C4—1224no—
522C4—2442no—
523C4—2441no—
524C4—2442no—
525C4#117×D6111yescharacteristic
526C4#1684023011yescharacteristic
527C4#1684030811yescharacteristic
528C4#1684030811yescharacteristic
529C2—21no—
530C2—21no—
531C2—81no—
532C2—4881no—
533C2#2144827811yescharacteristic
534C2#2145472612yes—
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2923C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C22
cosocleC22×C4×C61C24
hypercenter#2923D61
hypocenterC61#21297
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2923

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #21454468C2semidirect
5. #21446569C2semidirect
6. #21446564C2semidirect
7. #21446533C2semidirect
8. #21446529C2semidirect
9. #21446526C2semidirect
10. #21446522C2semidirect
11. #21445726C2semidirect
12. C4×#14519703C2semidirect
13. C4×#14519704C2semidirect
14. #97×Dic61C2semidirect
15. C61×#2923C2semidirect
18. #16839872C4semidirect
19. #16839867C4semidirect
20. #16839862C4semidirect
21. #16839860C4semidirect
264. #2923D61semidirect
326. C61#21297semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214546172
#214544682
#214467112
#214467062
#214465692
#214465642
#214465332
#214465292
#214465262
#214465222
#214457262
C4×#145197032
C4×#145197042
#97×Dic612
C61×#29232
#2129761